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A084750
Numbers k such that k! - p is a prime, where p is the smallest prime > k.
3
4, 5, 10, 11, 12, 14, 29, 53, 81, 90, 116, 236, 323, 346, 1172, 2957, 8400
OFFSET
1,1
COMMENTS
Numbers k such that k! - NextPrime(k) is prime.
If k != 3, there does not exist a prime p and a number k such that k! - NextPrime(k) < p < k! - 1. - Farideh Firoozbakht, Feb 26 2004
EXAMPLE
10 is in the sequence because 10! = 3628800, NextPrime(10) = 11 and 3628800 - 11 = 3628789 is prime.
MATHEMATICA
Do[If[PrimeQ[k!-NextPrime[k]], Print[k]], {k, 0, 1425}] (* Farideh Firoozbakht, Feb 26 2004 *)
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 16 2003
EXTENSIONS
More terms from Farideh Firoozbakht, Feb 26 2004
a(16) from Ryan Propper, Jul 09 2005
Edited by N. J. A. Sloane at the suggestion of Ryan Propper, Jan 26 2008
a(17) from Michael S. Branicky, Jun 21 2023
STATUS
approved